Goal:
  
  A : Type
  B : Type
  P : A → B → B → Type
  Q : A → B → B → Type
  H1 : ∀ (x : A) (y z : B), P x y z → Q x y z
  H2 : ∀ (x : A) (y : B), Q x y y
  b : A
  hd : B
  hd' : B
  a : B
  tl : list B
  p : P b hd hd'
  e : #|[]| = #|a :: tl|
  IHtl : ∀ bs : list A, #|bs| = #|tl| → All3 Q bs tl tl
  ============================
   (All3 Q [] (a :: tl) (a :: tl))


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:¬ _ |- _ => solve [ case H; trivial ]
              end ])